
vorschieben
to push forward
To move something forward by pushing it.
Er schob den schweren Riegel vor die Tür.
He pushed the heavy bolt in front of the door.
to push forward / use as a pretext
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to push forward
To move something forward by pushing it.
Er schob den schweren Riegel vor die Tür.
He pushed the heavy bolt in front of the door.

to use as a pretext
To use someone or something as a pretext or excuse in order to hide the real reasons or one's own responsibility.
Sie hat eine dringende Besprechung vorgeschoben, um nicht an dem unangenehmen Gespräch teilnehmen zu müssen.
She used an urgent meeting as a pretext so she wouldn't have to take part in the unpleasant conversation.

to push ahead
To push one's way forward in a line or group in order to get a better position.
Der ungeduldige Mann versuchte, sich in der Warteschlange vorzuschieben.
The impatient man tried to push ahead in the queue.
'Vorschieben' (to push forward / use as a pretext) is a separable verb with the prefix 'vor-'. In a main clause, the prefix goes at the end; in a subordinate clause, the verb stays together. In the infinitive with 'zu', 'zu' goes between 'vor' and 'schieben'.
Er schiebt den Tisch einen Meter vor.
He pushes the table one meter forward.
The verb consists of 'vor' (forward) and 'schieben' (to push). The literal meaning is 'to push forward.' The figurative meaning (to use an excuse) is derived from this: you symbolically push a reason in front of yourself in order to hide behind it.
Um nicht aufräumen zu müssen, schob er seine Kopfschmerzen vor.
To avoid having to tidy up, he used his headache as a pretext.
In the figurative meaning, 'vorschieben' is often used with abstract nouns. Typical combinations are 'eine Ausrede vorschieben' (to use an excuse as a pretext), 'einen Grund vorschieben' (to put forward a reason as a pretext), or 'einen Vorwand vorschieben' (to use a pretext).
Er hat einen dringenden Anruf vorgeschoben, um das Meeting früher zu verlassen.
He used an urgent call as a pretext to leave the meeting early.
In the meaning 'sich vordrängeln' (to push ahead / cut in line), the verb is always used reflexively with 'sich'. The reflexive pronoun must be adapted to the person (ich schiebe mich vor, du schiebst dich vor, etc.).
An der Kasse hat sich einfach jemand vor mich vorgeschoben.
At the checkout, someone simply pushed in ahead of me.